Isothermal and non-isothermal cure of a tri-functional epoxy resin (TGAP): A stochastic TMDSC study

Thermochimica Acta 529 (2012) 14–21

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Isothermal and non-isothermal cure of a tri-functional epoxy resin (TGAP): A stochastic TMDSC study John M. Hutchinson ∗ , Fatemeh Shiravand, Yolanda Calventus, Iria Fraga Departament de Màquines i Motors Tèrmics, ETSEIAT, Universitat Politècnica de Catalunya, Carrer Colom 11, 08222 Terrassa, Spain

a r t i c l e

i n f o

Article history: Received 7 September 2011 Received in revised form 8 November 2011 Accepted 9 November 2011 Available online 17 November 2011 Keywords: Differential scanning calorimetry (DSC) Epoxy TGAP TOPEM® Vitrification

a b s t r a c t The isothermal cure of a highly reactive tri-functional epoxy resin, tri-glycidyl para-amino phenol (TGAP), with diamino diphenyl sulphone (DDS), at two different cure temperatures Tc has been studied by both conventional differential scanning calorimetry (DSC) and by a stochastic temperature modulated DSC technique, TOPEM. From a series of isothermal cure experiments for increasing cure times, the glass transition temperature Tg as a function of isothermal cure time is determined by conventional DSC from a second (non-isothermal) scan, and the vitrification time tv is obtained as the time at which Tg = Tc . In parallel, TOPEM experiments at the same Tc lead directly to the determination of tv from the sigmoidal change in the quasi-static heat capacity. It is not possible to identify the glass transition temperature of the fully cured system, Tg∞ , in a third scan by conventional DSC. In contrast, with TOPEM a second (non-isothermal) scan at 2 K/min after the isothermal cure gives rise to three separate transitions: devitrification of the partially cured and vitrified material; almost immediate vitrification as the Tg of the system again rises; finally another devitrification, at a temperature approximating closely to Tg∞ . Thus with TOPEM it is possible to obtain a calorimetric measure of the glass transition temperature of this fully cured system. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Epoxy resins are versatile thermosetting polymers which are widely used in various applications, such as adhesives, surface protective coatings, encapsulation and as the matrix material for fibre reinforced composite materials. With respect to this last, the use of epoxy resins in high performance applications, and in particular in the aerospace and defence industries, makes severe demands on the material properties. The properties of particular interest here include high modulus, thermal stability and toughness. One epoxy system that has received considerable interest in this respect is based on the tri-functional epoxy resin, tri-glycidyl para-amino phenol (TGAP), which may be cured with either diamino diphenyl sulphone (DDS) or diethyl toluene diamine (DETA). As a result of the tri-functional nature of the epoxy monomer, these cross-linked materials have a high cross-link density and hence a high glass transition temperature. Another consequence of this high cross-link density is that these cured systems are inherently brittle, and for their practical applications it is necessary to increase their toughness. This can be achieved by incorporating thermoplastic modifiers [1–8] or rubber particles [9], for example. More recently, the use of hyper-branched polymers [10,11] and the incorporation of layered

∗ Corresponding author. Tel.: +34 93 739 8123; fax: +34 93 739 8101. E-mail address: [email protected] (J.M. Hutchinson). 0040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2011.11.008

silicates to form a nanocomposite [12–15] have been investigated. With respect to this last, in particular, the efficacy of this approach depends critically on the exfoliation of the layered silicate, which in turn depends on the cure kinetics of the epoxy resin. The study of the cure kinetics of this resin system is therefore of considerable importance. In the investigation of the cure kinetics of TGAP systems by differential scanning calorimetry (DSC), one of the unfortunate characteristics is that the very high degree of cross-linking leads to such a tightly bound three dimensional network structure that the glass transition temperature, Tg , of the fully cured system cannot be distinguished clearly in a conventional DSC scan [11,16]: the sigmoidal change in the heat flow, or heat capacity, is not evident with the sensitivity of the instrument. This is particularly clear from the isothermal cure results of Varley et al. [16]. In this work, for partially cured samples with a relatively low degree of cure, the network structure is sufficiently mobile, and a glass transition temperature can be measured in a second non-isothermal scan. On the other hand, for initial degrees of cure greater than 80%, for which the network structure is more tightly constrained, no glass transition is observed in a subsequent non-isothermal DSC scan. As a consequence, the usual procedure is to determine the glass transition for the fully cured system by dynamic mechanical analysis (DMA) instead of DSC, since DMA is a more sensitive technique [11,13]. However, this has the drawback that the glass transition temperature determined by DMA, for example from the peak temperature

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2.2. Sample preparation TGAP and DDS were mixed together in a small quantity by hand on a watch glass, using an excess epoxy ratio (1:0.9 molar ratio, 1:0.52 mass ratio, TGAP:DDS), as is often done [16] and is recommended by the materials manufacturer [23], for 5–7 min at 80 ◦ C on a hot-plate, and was then immediately degassed under vacuum at room temperature for 10–15 min. 2.3. Instrumental techniques

Fig. 1. Chemical structure of materials used in this study: (i) TGAP and (ii) DDS.

of tan ı, is frequency dependent, and usually measured at a frequency much higher than that equivalent to the usual heating rate employed for the determination of Tg by DSC [17–19], and hence is shifted to higher temperatures than would be found for a calorimetrically determined Tg . One of the promising applications of TGAP epoxy systems is as the matrix material of polymer layered silicate (PLS) nanocomposites [13]. For PLS nanocomposites, the exfoliation of the clay layers is presumed to take place during the cross-linking reaction of the epoxy, and hence the nanostructure development is intimately linked with the cure kinetics [20]. This reaction can be monitored by DSC, and a common cure schedule is first to cure only partially at a relatively low cure temperature, during which the sample vitrifies, and subsequently to complete a full cure either isothermally at a higher cure temperature or non-isothermally up to a sufficiently high temperature. While the glass transition temperatures of the partially cured samples can be determined by DSC, necessary for the complete study of the cure kinetics, the Tg of the fully cured sample cannot be so determined, for the reasons outlined above. There is clearly therefore an interest in developing a technique for the direct determination by a DSC technique of the glass transition temperature of fully cured TGAP epoxy systems. This is the purpose of the present paper. We show how a relatively new temperature modulated DSC (TMDSC) technique, known as TOPEM® and based not upon a periodically modulated heating rate but on a stochastic series of temperature pulses [21], can be used not only to follow the vitrification that occurs during the first isothermal scan but also to measure directly the glass transition temperature of the fully cured system during a subsequent non-isothermal scan.

2. Experimental 2.1. Materials The tri-glycidyl para-amino phenol (TGAP) epoxy resin, with trade name Araldite MY0510 (Huntsman Advanced Materials) and an epoxy equivalent between 95 and 106 g/eq, according to the manufacturer’s literature, was used without further purification. The epoxy equivalent was checked in our laboratory by titration, following standard procedures [22], and was found to be at the lower end of this range, with a value of 95 g/eq. The curing agent, 4,4-diamino diphenyl sulphone (DDS), with trade name Aradur 976-1 (Aldrich), was also used without further purification. The chemical structures of each of these products are shown in Fig. 1.

Two thermal analysis techniques were used: conventional differential scanning calorimetry (DSC821e, Mettler-Toledo), and TOPEM® (DSC823e, Mettler-Toledo). This latter is an advanced TMDSC technique in which stochastic temperature pulses are superimposed on the isotherm or on the underlying heating rate. It has been used for a variety of applications, including the study of the glass transition, isothermal curing of thermosets and solid–solid transitions [21], the physical aging of glass [24], the thermal degradation of polystyrene [25], and the characterisation of films formed by layer-by-layer synthesis [26]. The temperature amplitude of the pulses and the underlying heating rate are user-defined, and in this work values of ±0.5 ◦ C and 2 K/min, respectively, were used. The stochastic nature of these pulses is such that they are applied, alternately positive and negative, at random time intervals within user-defined minimum and maximum limits, known as the switching time range, which in this work was selected as 15–30 s. The advantages of TOPEM® are two-fold: first, it allows the determination of the so-called quasi-static specific heat capacity, cP0 , equivalent to the complex specific heat capacity of TMDSC but extrapolated to approximately zero frequency [21,27]; and second, it permits the separation of this quasi-static specific heat capacity into its frequency dependent components, which not only identifies those transitions which are frequency dependent and distinguishes them from those that are frequency independent, but also allows the frequency dependence to be determined quantitatively [27]. From an analysis of the correlation between the heating rate and heat flow, it is possible to obtain information about the dynamic behaviour of both the sample and the instrument, which ultimately yields cP0 and its frequency dependent components without the need for additional calibration procedures, which are required, for example, in other TMDSC techniques such as Alternating DSC (ADSC). In the TOPEM® results presented here, since we are interested principally in heat capacity changes, only relative values for cP0 are presented; it is possible to obtain accurate absolute values by TOPEM® if a calibrant such as synthetic sapphire is used. Each of the instruments used here was equipped with an intra-cooler (Haake EKL90/MT for the DSC821e, Julabo FT400 for the DSC823e) and was calibrated for both temperature and heat flow using indium. Samples were carefully weighed into standard aluminium crucibles, with sample masses typically in the range 8–10 mg for DSC and approximately 10–15 mg for TOPEM® . For isothermal cure experiments, the prepared TGAP/DDS samples were placed by robot into the DSC or TOPEM® cell, previously stabilised at the desired isothermal cure temperature in order to capture as much as possible of the initial part of the reaction. Isothermal cure experiments in the DSC were made at 120 ◦ C and 150 ◦ C, for cure times of 0.5, 1, 1.5, 2, 3, 4, 5 and 6 h in order to determine the evolution of the glass transition temperature of the partially cured system. The isothermal cure was immediately followed by a second, non-isothermal, scan from 50 ◦ C to 300 ◦ C, at 10 K/min in the DSC, in order to determine the glass transition temperature of the partially cured sample and to follow the residual cure reaction, which proceeds until the sample is fully cured. Finally, a third scan (non-isothermal, at 10 K/min over the same temperature range of 50–300 ◦ C) was made in the DSC in order

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to determine the glass transition temperature of the fully cured system. For the TOPEM® technique, isothermal cure experiments were made at 150 ◦ C for 3 h and at 120 ◦ C for 7.5 h. Immediately following these isothermal experiments, a second, non-isothermal, scan was made using TOPEM® , at a heating rate of 2 K/min over the temperature range of 50–300 ◦ C, and with the values of the other experimental parameters as defined above.

3. Results and discussion 3.1. Isothermal cure by conventional DSC A typical result for the isothermal cure at 150 ◦ C for 3 h of the TGAP/DDS system, followed by the second and third nonisothermal scans, obtained by conventional DSC is shown in Fig. 2. It can be seen that the reaction is initiated very quickly at this cure temperature, and that despite the precautions taken in the experimental procedure described above, some of the reaction is lost at the start. This is typical of the isothermal cure of such systems [11,16], but means that care must be exercised in the evaluation of the heat of reaction from such cure curves. Furthermore, although it is not possible to identify directly from the isothermal cure curve, vitrification occurs at some time and the reaction stops with the sample only partially cured. The degree of cure and, for some but not all of the isothermal cure times as will be shown shortly, the Tg of the partially cured sample can be determined from the second scan shown in Fig. 2(ii). Here, at around 180 ◦ C, the beginning of a sigmoidal endothermal change in the heat capacity, characteristic of a glass transition, can be seen to occur. However, this glass transition is incomplete, because (at least in the particular case illustrated here) almost concurrently the residual cross-linking reaction begins, with the consequence that the precise Tg of the partially cured sample cannot be determined, as is discussed in more detail below. The residual cure continues until the sample is fully cured, at a temperature of approximately 280 ◦ C, with the apparent onset of some degradation at higher temperatures. The residual heat of reaction, Hres , can be obtained from the area under this exotherm. A third scan, shown in Fig. 2(iii), should in principle permit the determination of the Tg of the now fully cured sample. However, the network structure of this highly cross-linked system is so rigid that no glass transition is discernible by DSC. Furthermore, the onset of degradation is again noticeable; the Tg of this system when fully cured is so high that its determination in a third scan almost inevitably involves some degradation. This difficulty is resolved by the use of TOPEM® , as will be shown below. When a series of cure times at 150 ◦ C is used, increasing from 0.5 h to 6 h, followed by a second scan in each case, the glass transition (or in some cases “apparent” glass transition) temperature of the partially cured sample, as well as some other characteristic features of the glass transition, can be determined as a function of the cure time. Fig. 3 shows the second scans for 6 different isothermal cure times within this range (note that for the shortest cure time the second scan started at 10 ◦ C rather than 50 ◦ C in order to include the glass transition for this sample). It can be seen from this figure that, for cure times of 0.5, 1 and 1.5 h, the glass transition appears unexceptional, the Tg increasing with increasing cure time, and hence with increasing degree of cure, while at the same time the width of the transition increases, indicative of a broadening of the relaxation time distribution in the early stages of the reaction, before vitrification occurs. The values of Tg as a function of cure time are collected in Table 1, from which it can be seen that for cure times up to 1.5 h there is no vitrification, as Tg is less than the isothermal cure temperature of 150 ◦ C. For longer isothermal cure times, however, and in

particular for the times of 3, 5 and 6 h shown in Fig. 3, vitrification does occur, since in all these cases the glass transition appears at a temperature higher than the cure temperature. Although each curve displays clear evidence of an underlying glass transition, though, these endothermic peaks do not strictly represent the glass transition, and hence a glass transition temperature cannot strictly be quantitatively assigned to any feature of these curves, such as the peak endothermic temperature or the mid-point temperature of the step change. For this reason, the values quoted in Table 1 for times greater than 2 h are shown shaded. There are two clear reasons for why these temperatures are not strictly glass transition temperatures. First, with increasing degree of cure, not only should Tg increase but also Cp should decrease [28]. The results in Table 1 show that this decrease does indeed occur up to vitrification, but that thereafter it apparently increases with increasing degree of cure. The explanation for this lies in the second reason mentioned above, which is that for cure times greater than 2 h the endothermic event is not a simple glass transition. When the glass transition temperature of the partially cured sample rises above the cure temperature of 150 ◦ C, the sample passes into a glassy state (vitrification). With increasing isothermal cure time beyond vitrification at this temperature, the degree of cure normally increases only very little, since the reaction is now diffusion controlled rather than chemically controlled and hence the reaction rate would normally be reduced dramatically. For this highly reactive TGAP resin, though, there appears to be the possibility that significant reaction continues to occur even after vitrification; according to Varley et al. [16] the high functionality of the TGAP resin means that there are likely to be reactive sites available even when they are locked into the network structure. This can explain in part why the endothermic peaks in Fig. 3 appear at temperatures up to 50 ◦ C higher than the isothermal cure temperature. There is additionally, however, another important effect, which is that the vitrified sample is continuously aging at the isothermal cure temperature, which is situated some tens of degrees below the glass transition temperature. The longer the cure time, the greater will be the amount of aging that takes place, and the enthalpy lost during this aging is recovered during the second scan, being manifest as an endothermic peak, which increases in magnitude and appears at a temperature which increases as the aging time, or cure time, increases [29–31]. The amount by which this endothermic peak shifts with aging time depends on several material parameters, including the non-exponentiality parameter, ˇ, but in particular on the non-linearity parameter, x [30,31]; the smaller is x, the greater is the non-linearity, and the greater is the amount of this shift. In this system, it appears that the kinetics of the aging process is governed by a small value of x in view of the substantial amount by which this peak temperature shifts. This effect can be simulated by incorporating the enthalpy relaxation effect into a model for the kinetics of the cure reaction in which vitrification occurs, while further evidence for there being a small value for x will appear shortly. The endothermic peaks which are seen for cure times of 3, 5 and 6 h in Fig. 3 are just such aging or enthalpy relaxation peaks, and cannot therefore be used as a quantitative measure of the glass transition temperature. This explains why cp appears to increase for these cure times: the step change used for the determination of cp in Table 1 is really the rise of the enthalpy relaxation peak, and is an incorrect determination of cp . The results shown in Fig. 3 and summarised in Table 1 allow the vitrification time for this system at 150 ◦ C to be found, defined as the cure time for which the glass transition temperature is equal to the isothermal cure temperature. The glass transition temperatures in Table 1 are plotted as a function of cure time in Fig. 4. Even though the Tg values for tc greater than or equal to 3 h are not strictly glass transition temperatures, nevertheless a smooth curve

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Fig. 2. Cure of TGAP/DDS system by DSC: (i) isothermal cure at 150 ◦ C for 3 h; (ii) second scan at 10 K/min; (iii) third scan at 10 K/min. Exothermic direction is upwards.

Fig. 3. Second scans at 10 K/min in DSC after various isothermal cure times at 150 ◦ C, as indicated: 0.5, 1, 1.5, 3, 5, 6 h. Exothermic direction is upwards.

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Table 1 Collected data from second DSC scan after isothermal cure at 150 ◦ C for the times indicated. Cure time (h)

Tg (◦ C) cp (J/gK) Hres (J/g) Vitrification

0.5

1

1.5

2

3

4

5

6

23.3 0.57 456 No

94.5 0.38 254 No

139.2 0.13 170 No

158.0 0.13 134 Yes

175.8 0.19 123 Yes

186.4 1.19 121 Yes

194.2 0.67 112 Yes

198.1 0.91 107 Yes

The shaded values are unreliable values because they are influenced by enthalpy relaxation during isothermal cure. Table 2 Collected data from second DSC scan after isothermal cure at 120 ◦ C for the times indicated. Cure time (h)

◦

Tg ( C) cp (J/gK) Hres (J/g) Vitrification

2

3

4

5

6

7.5

17.9 0.55 491 No

52.1 0.48 359 No

89.2 0.38 265 No

112.6 0.30 201 No

130.6 0.30 192 Yes

138.2 0.51 167 Yes

The shaded values are unreliable values because they are influenced by enthalpy relaxation during isothermal cure.

drawn through all these points will define a vitrification time, tv , since Tg values for times shorter than tv are true glass transition temperatures. This construction gives a value of 103 min (1.7 h) for tv at the isothermal cure temperature of 150 ◦ C. It is interesting to consider here the procedure proposed by Gillham and co-workers [32] for the erasure of the effects of physical aging during the isothermal cure. After curing isothermally at 150 ◦ C for 3 h, the “apparent” Tg of the partially cured sample is 175.8 ◦ C, as seen in Fig. 3 and given in Table 1. If the effects of physical aging are erased by previously heating the partially cured sample to its apparent Tg and then cooling it again to 50 ◦ C, a subsequent non-isothermal scan in the DSC at 10 K/min gives an even higher glass transition temperature of about 185 ◦ C. Clearly what is happening in this system is that further significant cure occurs, following a chemical controlled kinetics, even when the cure temperature is significantly below the glass transition temperature, in a regime where diffusion controlled kinetics would normally be anticipated. The same conclusion will be reached from a consideration of the TOPEM results to be presented later in Fig. 6, and serves to emphasise the unusual reaction behaviour of this TGAP/DDS system. Similar results were obtained also at a lower cure temperature of 120 ◦ C, and are collected in Table 2. Here again, it can be seen that cp first decreases with increasing cure time, and then begins to increase, for the reasons explained earlier. Using the same procedure as above, the vitrification time for cure at 120 ◦ C in this system is found to be 324 min (5.4 h).

These results show that conventional DSC allows the determination of the vitrification time in the isothermal cure of this system, but that it is a lengthy procedure. On the other hand, though, it is not possible to find the glass transition temperature of the fully cured system, since the network structure is too rigid for there to be any clear indication of a Tg in the third scan, as can be seen in Fig. 2(iii). In contrast, the use of TOPEM® , the results of which are shown immediately below, allows both a real-time evaluation of the vitrification and a clear identification of the glass transition of the fully cured system.

3.2. Isothermal cure by TOPEM® The TOPEM® technique uses a stochastic modulation of the temperature programme by means of random small pulses of temperature, alternately positive and negative; in the present case, these pulses are superimposed on the isotherm, at either 120 ◦ C or 150 ◦ C. In addition to measuring the heat flow, TOPEM® also determines the so-called frequency-independent heat capacity, Cp0 , equivalent to the complex heat capacity of temperature modulated DSC, but (in principle) extrapolated to zero frequency [21]. Although in some earlier work with TOPEM® we proposed [27] that this limiting frequency was of the order of 4 mHz rather than zero, Cp0 is nevertheless an instantaneous heat capacity, which reflects the molecular and structural changes taking place in the curing sample, and which can be separated into its frequency dependent

Fig. 4. Glass transition temperature (or apparent glass transition temperature) as a function of cure time at 150 ◦ C.

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Fig. 5. TOPEM® isothermal cure at 150 ◦ C for 3 h: upper curve, heat flow; lower curve, quasi-static specific heat capacity cp0 . Experimental parameters: pulse amplitude ± 0.5 ◦ C, switching time range 15–30 s.

components. As an illustration, Fig. 5 shows an isothermal TOPEM® scan for isothermal cure at 150 ◦ C for a cure time of 3 h. In this isothermal cure experiment, the constant amplitude pulses give rise to a smooth envelope, the amplitude of the heat flow changing as the instantaneous heat capacity changes. On the other hand, there is an irregularity on the time scale, resulting from the random selection of the time interval between pulses (the switching time); it is this which permits the separation of Cp0 into its frequency dependent components. The overall cure response can be identified from the average of the heat flow envelope, and is clearly the same as that obtained by conventional DSC and shown in Fig. 2(i), displaying a peak exotherm at a cure time of just less than 30 min. In addition, though, the vitrification is also clearly evident as a change in the amplitude of the heat flow envelope as

the system changes from a liquid to a glassy state, with a consequent reduction in the instantaneous heat capacity. In TOPEM® this is more clearly shown as the sigmoidal reduction of Cp0 , which is superimposed on the heat flow modulations in Fig. 5. From this heat capacity change, the vitrification time can be determined directly as the time at which it attains a value mid-way between the extrapolated liquid and glass values, as shown by the construction in Fig. 5. This gives a vitrification time of 100.27 min, in excellent agreement with the value obtained above by conventional DSC. A similar result was obtained for the isothermal cure by TOPEM® at 120 ◦ C, for which a vitrification time of 330 min was found, again in excellent agreement with the DSC result. It should be borne in mind, though, that the vitrification time determined in this way by TOPEM® , or indeed by any TMDSC

Fig. 6. TOPEM® second scan at 2 K/min: upper curve, heat flow; lower curve, quasi-static specific heat capacity cp0 . Experimental parameters: pulse amplitude ± 0.5 ◦ C, switching time range 15–30 s.

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technique [33], is a function of the frequency of the measurement. In the present case, this frequency is that applicable to the quasi-static heat capacity, Cp0 , which has been estimated to be approximately 4 mHz. On the other hand, the vitrification time is found by conventional DSC on heating after cooling at a certain rate, in the present case at 20 K/min. The particular values of frequency, f [Hz], and cooling rate, q [K/s], may not correspond to the same vitrification time, however. The equivalence between these two parameters is established by an equation [17,34,35] based upon the fluctuation dissipation theorem of the glass transition [36–38], which may be written in the form: ω=

|q| a␦T

(1)

In this equation, ω [rad/s] is the angular frequency of modulation [ω = 2f], a is a constant, commonly found to be of the order of 6 ± 2 for typical glass-forming systems, and ␦T is the mean temperature fluctuation of the cooperatively rearranging regions. The present results for which a frequency of 4 mHz corresponds to a cooling rate of 20 K/min imply that a␦T = 13.3 K. From numerical simulations of the glass transformation process in DSC and TMDSC [see Table 2 in Ref. 18], it can be seen that such a value of a␦T implies a low value of the non-linearity parameter, x, in agreement with the earlier observation that long isothermal cure times lead to a significant shift of the peak endotherm temperature in the subsequent second scan. Thus partially cured TGAP/DDS represents a system with a high degree of non-linearity in its structural relaxation behaviour, and could be an interesting candidate for further enthalpy relaxation studies, in particular in comparison with the same TGAP/DDS system in which nanoclay is incorporated. However, not only is TOPEM® advantageous with respect to the determination of the vitrification time in this system, but also it can be used to great advantage in the subsequent second scan, as has been demonstrated earlier by Van Mele and co-workers in respect of the application of TMDSC to cure, vitrification and devitrification in thermosetting systems [39–41]. A typical second scan by TOPEM® is shown in Fig. 6 where in the upper curve the modulated heat flow can be seen and in the lower curve the quasi-static specific heat capacity, cp0 , is shown. Three separate transitions are evident. The first, at 180.1 ◦ C, represents the devitrification of the partially cured sample, which is initially in a glassy state. Since TOPEM is a temperature modulated DSC technique, and the cP0 trace corresponds essentially to the reversing component of the heat flow, this devitrification transition should not be significantly dependent on the effects of aging that have taken place during the relatively short period of time that the system was vitrified in the previous isothermal cure at 150 ◦ C [42]. It is remarkable, therefore, that this glass transition occurs at a temperature some 30 ◦ C higher than the original cure temperature. What is happening here is that the slow heating rate of TOPEM allows sufficient time for the cure reaction to continue in this particular reacting system, which has the unusual ability to continue curing significantly even when the system is in the glassy state. This observation confirms that obtained earlier when the effects of aging were erased in conventional DSC following Gillham’s procedure [32]. Subsequent to this devitrification transition, the heat capacity increases on passing from the glassy to the rubbery state, but almost immediately, as the underlying temperature increases, the residual cure reaction of the system is initiated, with a consequent increase in the heat flow, as seen in the upper curve. This in turn leads to a further vitrification of the system as the glass transition temperature increases with the degree of cure, ˛, and a second transition is therefore seen, at 195.2 ◦ C. As the cure temperature continues to increase at the prescribed underlying rate, so also does the glass transition temperature increase, but the difference between the cure temperature and the glass transition

temperature remains small, so that the cure reaction proceeds. The residual cure in this case occurs at an almost constant rate, as seen in the upper curve of Fig. 6, rather than displaying the usual exothermic peak as observed in a second scan at 10 K/min in DSC, such as those shown in Fig. 3. Finally, as the degree of cure approaches 100%, the rate of increase of the glass transition temperature reduces, and the system devitrifies, passing from a glassy state back to a rubbery state, at a temperature of 256.5 ◦ C. At the same time, the residual cure reaction is completed, and the heat flow curve returns to the baseline, as seen in the upper curve of Fig. 6. The processes of vitrification and devitrification during nonisothermal cure, which correspond to the second and third transitions in Fig. 6, have been studied previously using TMDSC by Van Mele and co-workers [39–41] for bi-functional and tetrafunctional epoxy-amine systems, and using TOPEM® by our own group [43] for a DGEBA-diamine system, and the experimental results have been compared with a theoretical model [44]. It was shown that the temperature at which devitrification occurs is very close to the glass transition temperature of the fully cured system, Tg∞ , and more so the slower is the underlying heating rate of the non-isothermal cure. Thus we may take the devitrification temperature to be a good approximation to Tg∞ , and the results obtained for the samples initially cured isothermally at 120 ◦ C and 150 ◦ C are found to be 252.9 ◦ C and 256.5 ◦ C, respectively. A further advantage of this evaluation of Tg∞ during the second scan of TOPEM® is that it is determined before the onset of any degradation, which is seen in Fig. 2. These glass transition temperatures are determined calorimetrically for this TGAP/DDS system, which has hitherto not been possible by conventional DSC, and which hence represents an important advantage of TOPEM® . At present, it is not possible to say whether the difference between these two values of Tg∞ is significant, and a consequence of there being an effect of the previous isothermal cure temperature. There are two experimental aspects to consider here. First, the determination of each of these two values is subject to some experimental uncertainty, as is evident from a consideration of the construction of the asymptotes shown in Fig. 6. And second, the approximation of the devitrification temperature to Tg∞ depends on the underlying heating rate in TOPEM® . This latter appears to have little effect here, however, as a repeat TOPEM® second scan after isothermal cure at 150 ◦ C, but using the slower rate of 0.5 K/min, which in principle allows a closer approximation to Tg∞ to be achieved, results in essentially the same value of 255.8 ◦ C. Comparison of these Tg∞ values with others in the literature is interesting. Frigione and Calò [11] report a value of 245.4 ◦ C for TGAP cured with diamino diethyl toluene (DETDA), this value being determined by DMA at a frequency of 1 Hz. Varley et al. [16] find, for TGAP cured with DDS, a value of about 264 ◦ C by DMA at an unspecified frequency. This last value is slightly greater than those found here, but it must be borne in mind that the DMA value is anticipated to be greater than the calorimetric value on account of the effect of the frequency of measurement. Indeed, Varley et al. show that, for the partially cured samples, Tg measured by DMA is on average about 10 ◦ C higher than that measured by DSC, thus giving a good correspondence between their result and ours. Furthermore, for the partially cured system, the value of Tg is essentially independent of the isothermal cure temperature when samples with the same degree of cure are compared, while the Tg of the fully cured system, defined by the peak in tan ␦, is also independent of the previous isothermal cure temperature. These authors conclude that the cure mechanism is independent of the cure temperature, in agreement with Wang and Gillham [45], so that Tg is a function only of the degree of cure, which implies a unique value for Tg∞ .

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4. Conclusions The technique of TOPEM® has been shown to have significant advantages over conventional DSC in characterising the isothermal cure of a tri-functional epoxy resin system, TGAP/DDS. The cure schedule for such systems typically includes isothermal cure at a temperature less than the glass transition temperature of the fully cured system, Tg∞ , so that vitrification occurs. Furthermore, the network structure produced after full cure is so tight that Tg∞ cannot be determined by conventional DSC. The advantages of TOPEM® are: first, that vitrification can be identified directly during isothermal cure, with the direct measurement of the corresponding vitrification time; and second, that a good approximation to Tg∞ can be determined from a non-isothermal TOPEM® scan after the partial isothermal cure. The results obtained by TOPEM® for Tg∞ are in good agreement with values obtained by dynamic mechanical analysis by other authors. In addition, comparison of the frequency-dependent vitrification time obtained by TOPEM® and the rate-dependent vitrification obtained by conventional DSC shows that the partially cured TGAP/DDS system displays a highly non-linear enthalpy relaxation behaviour, which may also apply to the fully cured system and which is worthy of further investigation. Acknowledgements This work was supported by a grant from the Spanish Ministry of Education and Science, MAT 2008-06284-C03-03. We are grateful to Huntsman Advanced Materials for the provision of the TGAP epoxy resin. References [1] C.B. Bucknall, I. Partridge, Phase-separation in epoxy-resins containing polyethersulfone, Polymer 24 (1983) 639–644. [2] C.B. Bucknall, Toughening tetrafunctional epoxy-resins using polyetherimide, Polymer 30 (1989) 213–217. [3] D.J. Hourston, J.M. Lane, The toughening of epoxy-resins with thermoplastics. 1. Trifunctional epoxy-resin polyetherimide blends, Polymer 33 (1992) 1379–1383. [4] A.J. MacKinnon, S.D. Jenkins, P.T. McGrail, R.D. Pethrick, A dielectric, mechanical, rheological, and electron-microscopy study of cure and properties of a thermoplastic-modified epoxy-resin, Macromolecules 25 (1992) 3492–3499. [5] J.G. Jang, W. Lee, Polyetherimide-modified high-performance epoxy-resin, Polym. J. 26 (1994) 513–525. [6] R.J. Varley, J.H. Hodgkin, G.P. Simon, Toughening of a trifunctional epoxy system. Part VI. Structure property relationships of the thermoplastic toughened system, Polymer 42 (2001) 3847–3858. [7] J. Zhang, Q. Guo, B.L. Fox, Study on thermoplastic-modified multifunctional epoxies: influence of heating rate on cure behaviour and phase separation, Compos. Sci. Technol. 69 (2009) 1172–1179. [8] B.K. Kandola, B. Biswas, D. Price, A.R. Horrocks, Studies on the effect of different levels of toughener and flame retardants on thermal stability of epoxy resin, Polym. Degrad. Stabil. 95 (2010) 144–152. [9] M. Frigione, D. Acierno, L. Mascia, Miscibilization of low molecular weight functionalized polyethylenes in epoxy resins. I. Effects of composition and modifications chemistry, J. Appl. Polym. Sci. 73 (1999) 1457–1470. [10] D. Ratna, R. Varley, G.P. Simon, Toughening of trifunctional epoxy using an epoxy-functionalized hyperbranched polymer, J. Appl. Polym. Sci. 89 (2003) 2339–2345. [11] M. Frigione, E. Calò, Influence of an hyperbranched aliphatic polyester on the cure kinetic of a trifunctional epoxy resin, J. Appl. Polym. Sci. 107 (2008) 1744–1758. [12] O. Becker, R. Varley, G. Simon, Morphology, thermal relaxations and mechanical properties of layered silicate nanocomposites based upon high-functionality epoxy resins, Polymer 43 (2002) 4365–4373. [13] O. Becker, Y.B. Cheng, R.J. Varley, G.P. Simon, Layered silicate nanocomposites based on various high-functionality epoxy resins: the influence of cure temperature on morphology, mechanical properties, and free volume, Macromolecules 36 (2003) 1616–1625. [14] O. Becker, R.J. Varley, G.P. Simon, P.J. Halley, Layered silicate nanocomposites based on various high-functionality epoxy resins: The influence of an organoclay on resin cure, Polym. Eng. Sci. 43 (2003) 850–862.

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